
Volume 48, Number 56, 2003


Issue honoring Prof. Dr. A.A. Raduta on his 60^{th} Anniversary 

Page 
Title & Author(s) 
519 
Preface


521 
Foreword


523 
Bilocal Dynamics in Quantum Field Theory
Ciprian Acatrinei
An essential aspect of noncommutative field theories is their bilocal nature. This feature, and its role in the IR/UV mixing, are discussed using a canonical quantization procedure developed recently.


529 
Discrete Group Symmetry in the Fast Chebyshev Transform
Gh. Adam, S. Adam
We consider nonadaptive ClenshawCurtis (CC) quadrature of variable degree n=2m, m = 2, 3, .... The computation of the coefficients of the truncated Chebyshev series expansion of the integrand is shown to be done accurately and efficiently within a fast Chebyshev algorithm. It takes into account the binary tree structures with heap ordering key of the coefficients, the splitting of the n $\times$ n coefficient matrix into irreducible $2^l \times 2^l$ blocks, where $l$ denotes the depth level of the children inside the heap, and the group symmetry properties which can be defined inside each block.


537 
What Can We Learn from the Instabilities of Asymmetric Nuclear Matter?
V. Baran, M. Colonna, M. Ditoro, V. Greco
Based on a general approach to binary systems we show that in low density region asymmetric nuclear matter (ANM) is unstable only against isoscalarlike fluctuations. The physical meaning of the thermodynamical chemical and mechanical instabilities is related to the inequality relations verified by the strength of interaction among different components. Relevance of these results for bulk and neck fragmentation in the reaction $^{124}$Sn + $^{124}$Sn at 50 MeV/$n$ is discussed.


545 
Differential Operators on Orbits of Coherent States
S. Berceanu, A. Gheorghe
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space attached to the dual of the Hilbert space of the representation. This permits a realization of coherent state Lie algebras by firstorder differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits.


557 
Exact Results for a Model Ternary Solution with Strong ThreeBody Interactions
Florin D. Buzatu, Dale A. Huckaby
We consider a lattice model for threecomponent systems in which the lattice (honeycomb or threecoordinated Bethe) bonds are covered by molecules of type AA, BB, and AB, and the only interactions are between the molecular ends of a common lattice site. The model reduces to a standard Ising model on the original honeycomb or Bethe lattice and the exact coexistence curves for phase separation have been previously calculated for weak threebody interactions. In the present paper we analyze by the same technique the case of strong threebody interactions, the difference being that now the Ising parameters on the intermediate lattice are complex. Exact, closedform expressions are obtained for the twophase coexistence surface in temperaturecomposition space. The exact coexistence curves are drawn for various values of a reduced threebody coupling constant and the reduced temperature. We show there is no phase separation in the model on the considered lattices for sufficiently large threebody coupling constant.


567 
An Analytical Solution for the Inverse Conductivity Problem
S. Ciulli, M. K. Pidcock, C. Sebu
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. By using a priori information we are able to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind and then by solving a first order partial differential equation for the conductivity $\sigma(x)$. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.


583 
Polarized Dirac Fermions in de Sitter Spacetime
Ion I. Cotăescu
The tetrad gauge invariant theory of the free Dirac field in two moving frames of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions of the Dirac equation with given momentum and helicity are derived and the final form of the quantum Dirac field is established.


597 
Quantum Phase Transitions: A Renormalization Group Approach
M. Crişan, I. Grosu, D. Bodea, I. Tifrea
We applied the Renormalization group method at finite temperature in order to study the $d$dimensional dilute Bose gas. The flowequations and the free energy are obtained for the case of arbitrary dimension, $d$, and the case $d = 2$ has been analyzed in the limit of low and high temperatures. The critical temperature, the coherence length and the specific heat are obtained for this particular case using a regular solution for the coupling constant, which is obtained from the scaling equations. A nonuniversal behavior, consisting in a logarithmic temperature dependence in the critical region has been obtained for the specific heat.


607 
SelfConsistent Description of Cold Fission Processes
D.S. Delion, A. Săndulescu, Ş. Mişicu, W. Greiner
We give a description of cold fision processes within the stationary scattering formalism. We predict a strong dependence of binary decay widths for $^{252}$Cf upon the internal structure of the considered resonant state. We also describe the spontaneous ternary cold fission of $^{252}$Cf, accompanied by $^4$He, $^{10}$Be and $^{14}$C. We have shown that angular distribution of the emitted light particle is strongly connected with its deformation and the equatorial distance.


619 
On the Parametrization of Complex Hadamard Matrices
P. Diţă
Complex Hadamard matrices are important in the mathematical structure of the quantum information theory being an essential tool for the construction of bases of unitary operators used in the theory. In this paper we provide a procedure for the parametrization of the complex Hadamard matrices for an arbitrary integer $n$ starting from our previous results on parametrization of unitary matrices. More precisely we obtain a set of $(n2)^2$ equations whose solutions give all the complex Hadamard matrices of size $n$.


627 
Some Applications of Riemannian Submersions in Physics
Maria Falcitelli, Stere Ianuş, Anna Paria Pastore, Mihai Vişinescu
We review some applications of Riemannian submersions in physics. We describe a compactification scheme for the KaluzaKlein theory triggered by a scalar sector in the form of a nonlinear sigma model. Another application refers to the KaluzaKlein monopole which was obtained by embedding the TaubNUT gravitational instanton into fivedimensional KaluzaKlein theory.


639 
ExtremeRelativistic Cross Sections for Compton Scattering by KShell Electrons
V. Florescu, M. Gavrila
We report on progress of our project on extreme relativistic (ER) Compton scattering of very hard incident photons ($\hbar \omega \gg mc^2$) from bound electrons. We have considered the case of a Coulomb atomic potential, of arbitrary nuclear charge Z. The calculation of the ER form of the Smatrix element was done with an analytical method. In the present case, this is a viable alternative to an impracticable ab initio numerical computation. In order to obtain the dominant behavior of the matrix element in the large $\omega_1$ limit, the momentum transferred to the nucleus $\Delta$ need be ascribed a constant (albeit arbitrary) value in the limiting process. The result depends critically on the spectral range in which the scatteredphoton energy $\omega_2$ is situated. We have considered the $\omega_2$ range covering the Compton line, for which the ratio $\omega_2/\omega_1$ need be kept finite. The triply differential cross section, $\mathrm{d}^3 \sigma_{ER}/\mathrm{d}\omega_2\mathrm{d}\Omega_2\mathrm{d}\Delta$, was calculated for the range of Compton line in terms of hypergeometric Appell functions. This is a rather unique example of a most elaborate Coulomb problem that could be solved analytically, in closed form. Finally, we report numerical results for the triply differential cross section, that has attracted theoretical and experimental interest recently.


649 
A Linear Kinetic Approach and Near Equilibrium Thermodynamics of Serum Parameters from AtherosclerosisInduced Animals Treated with Drugs
Alexandru Glodeanu, Anca Sima


657 
A Particular Case of Exotic Resonant States: DiNuc1ear Parent Quasimolecular States
N. Grama, C. Grama, I. Zamfirescu
The properties of the parent quasimolecular states are deduced from the general properties of the exotic resonant states found by the Riemann surface approach to Smatrix poles.


669 
Influence of Third Order Dispersion on the Bound State of Two Solitons of the NLS Equation
D. Grecu, Anca Vişinescu
Using KarpmanSolov’ev perturbation procedure the influence of the third order dispersion on the bound state of two solitons of the NLS equation is investigated. The problem has two small parameters (supposed to be of the same order): the small overlap of the two well separated solitons, and the amplitude of the third order dispersion. If the velocities of the two solitons are the same, a bound state is formed, with an oscillating expression for the distance between solitons. When the third order dispersion is introduced a slow monotonous increasing function of time is superposed over this oscillatory behaviour.


679 
Monotonicity Methods in the Nonlinear Kinetic Theory
C.P. Grünfeld
This paper reviews results on the existence theory of solutions for a class of kinetic models, recently introduced as generalizations of the classical Boltzmann equation. The problem of the existence, uniqueness and positivity of global solutions can be investigated by extending monotonicity methods, developed for solving the classical Boltzmann equation.


689 
A Statistical Mechanical Study of Phase Transitions on Crystalline Electrodes
Dale A. Huckaby, Igor Medved, Lesser Blum, Marc D. Legault
A microscopic statistical mechanical lattice gas model is used to study phase transitions that occur at the fluidcrystal interface during electrodeposition on a crystalline electrode surface. Current versus voltage plots, or voltammograms, constructed from the adsorption isotherms of the model agree quite well with experiment. The effects of finite sized electrode crystals on the shapes of voltammogram spikes associated with first order phase transitions are studied using the rigorous PirogovSinai theory.


697 
Study of the Optimization Possibilities of the Numerical Simulations of Some Physical Processes
Dan Iordache, Viorica Iordache


705 
Uncertainty Relations in the Theory of Open Quantum Systems
A. Isar
In the framework of the Lindblad theory for open quantum systems we derive analytical expressions of the Heisenberg and Schrödinger generalized uncertainty functions for a particle moving in a harmonic oscillator potential. The particle is initially in an arbitrary correlated coherent state and interacts with an environment at finite temperature. We analyze the relative importance of quantum and thermal fluctuations and show that the system evolves from a quantumdominated to a thermaldominated state in a time which is of the same order as the decoherence time.


717 
Fine Structure of Radiation Spectrum of Charged Particles Moving in Magnetic Fields in Nonabsorbable Isotropic Media and in Vacuum
A.V. Konstantinovich, S.V. Melnychuk, I.A. Konstantinovich
Integral expressions for spectral distributions of the radiation power for systems of noninteracting point charged particles moving on arbitrary trajectory in electromagnetic fields in nonabsorbable media and in vacuum are obtained using the Lorentz’s selfinteraction method. The fine structure of spectra of synchrotron, Cherenkov, and synchrotronCherenkov radiations of electrons moving in a spiral are investigated with analytical and numerical methods.


727 
Entanglement and Teleportation of Gaussian States of the Radiation Field
Paulina Marian, Tudor A. Marian, Horia Scutaru
We propose a reliable entanglement measure for a twomode squeezed thermal state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable states of the same kind. The requisite Uhlmann fidelity of a pair of twomode squeezed thermal states is evaluated as the maximal transition probability between two fourmode purifications. By applying the PeresSimon criterion of separability we find the closest separable state. This enables us to derive an insightful expression of the amount of entanglement. Then we apply this measure of entanglement to the study of the BraunsteinKimble protocol of teleportation. We use as input state in teleportation a mixed onemode Gaussian state. The entangled state shared by the sender (Alice) and the receiver (Bob) is taken to be a twomode squeezed thermal state. We find that the properties of the teleported state depend on both the input state and the entanglement of the twomode resource state. As a measure of the quality of the teleportation process, we employ the Uhlmann fidelity between the input and output mixed onemode Gaussian states.


743 
Analytical Solutions of a Dirac Bound State Equation and Their Relativistic Interpretation
L. Micu
We solve the single particle Dirac equation with a particular confining potential and comment its relativistic significance. We show that the solutions describe a complex physical system made of independent constituents: a free particle and an effective field representing the confining potential.


751 
Optical Spatiotemporal Solitons: Past, Present and Future
D. Mihalache
A brief overview of the field of optical spatiotemporal solitons („light bullets”) is given.


757 
Generalizing the $q$Symmetrized HarperEquation
C. Micu, E. Papp
The $q$symmetrized Harperequation [P. B. Wiegmann and V. A. Zabrodin, Phys. Rev. Lett. 72, 1890 (1994)] is generalized by accounting for arbitrary values of the anisotropy parameter $\Delta$. This parameter discriminates between metallic ($\Delta < 1$) and insulator ($\Delta > 1$) phases. Assuming that the wavefunction is described in terms of Laurent series, we succeeded to establish reasonable extrapolations of energy polynomials towards continuous values of the commensurability parameter, now for arbitrary $\Delta$values.


763 
Quantum Master Equation for a System of Charged Fermions Interacting with the Electromagnetic Field
Eliade Ştefănescu
A quantum master equation with microscopic coefficients is proposed to describe the dissipative dynamics of a Fermi system coupled with an environment of particles through a twobody potential. In comparison with other master equations existing in the literature, this equation satisfies the conditions of a dynamical detailed balance, leading to Pauli master equations for the diagonal elements of the density matrix, and to damped BlochFeynman equations for the nondiagonal ones during the whole evolution of the system. The new equation is particularized for a harmonic oscillator coupled with the electromagnetic field through electricdipole interaction and is compared with the wellknown equation of Săndulescu and Scutaru.


771 
Neutrino Masses from DoubleBeta Decay
S. Stoica, H.V. KlapdorKleingrothaus
We make a systematic study of the neutrinoless doublebeta decay matrix elements (ME) for several nuclei of experimental interest. The calculations are performed with the second quasi random phase approximation (SQRPA) methods. A better stability against the change of the s.p. basis used and a good fulfillment of the Ikeda Sum Rule allow to reduce the uncertainties in the values of the neutrinoless ME predicted by the QRPAbased methods to about 50% of their calculated values. Further, using the most recent experimental limits for the neutrinoless halflives, we derive new upper limits for the neutrino masses. These are in agreement with the recent claim of experimental evidence for neutrinoless doublebeta decay.


781 
Transmittance through an AharonovBohm Ring with Embedded Quantum Dot Described by Kondo Hamiltonian
M. Tolea, V. Dinu
Kondo physics of quantum dots together with the transmittance phase behavior are of considerable current interest, both experimentally [1] and theoretically [2]. The presence of magnetic impurities in the Q.D. produces new effects (like the spinflip scattering) due to the exchange interaction between the spin of the conducting electrons and the localized spins. We numerically find the complex transmittance of a Q.D. directly connected to leads or embedded in an AB ring, as in recent experimental devices used to calculate the phase (whose behavior has not been fully understood). The magnetic flux through the ring and gate potential applied on the dot are varied. We use a tightbinding model for the Kondo Hamiltonian and the LandauerBüttiker transport formalism [3] for the ringdot system (and the results can be seen as predictions of such a model).


787 
Randomness Effects on Modulational Instability of a Discrete SelfTrapping Equation
Anca Vişinescu, D. Grecu
The discrete selftrapping equation (DST) represents a useful model for several properties of onedimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view, considering the oscillator amplitude as a random variable. A kinetic equation for the twopoint correlation function is written down, and its linear stability is studied. Both a Gaussian and a Lorentzian form for the initial unperturbed wave spectrum are discussed. Comparison with the continuum limit (NLS equation) is done.


795 
SelfDual Gauge Theories
Gheorghe Zet
A model of spherically symmetric SU(2) gauge theory is considered. The selfduality equations are written and it is shown that they are compatible with the EinsteinYangMills equations. It is proven that the SU(2) gauge model is selfdual on a Schwarzschild spacetime but not on a ReissnerNordstrom one.


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